Math 095 Quiz 1 Circle your answers 1. Find the slopes of lines l1 and l2 that pass through the two given points. l1: (0, 0) and (–2, 4); l2:(3, 1) and (–1, –1) Then identify if the lines are parallel, perpendicular or neither. Graph the lines. 2. Write this equation in slope‐intercept form. Then identify the slope and y‐intercept. Graph the line. 2x − 3 y = 6 3. Use the point‐slope formula to write an equation of the line given the following information. Write the final answer in slope‐intercept form. The slope is 3, and the line passes through the point (1, –1). Graph the line. 4. Find an equation for the line by any method given the following information: The line passes through the point (2, 3) and is perpendicular to the line : y = 5 . Graph the line. (Hint: graph the lines first) 5. The electric bill charge for a certain utility company is $0.095 per kilowatt‐hour. The total cost, y, depends on the number of kilowatt‐hours, x, according to the equation: y = 0.095 x . a. Which variable is the independent variable? cost or kilowatt‐hour (circle one of these) b. Which variable is the dependent variable? cost or kilowatt‐hour (circle one of these) c. Determine the cost of using 500 kilowatt‐
hours. Name:___________________________ 1 2 3 4 Quiz 2 Chapter 7 Solving systems of equations Name: ___________________________ Solve by the method specified. Show all work, including check, for full credit Circle your answers 1. Solve this system by graphing: x + y = 5 y =
3
x − 2 4
2. Solve this system by substitution: 4x = 3 y y =
4
x + 2 3
3. Solve this system by addition: 6x − 2 y = 6
4 y = −2 x + 2
Quiz 3 Chapter 8 Name: __________________________________________ Show all work. Circle your answers 1. Given f ( x) = − x 2 − 2 x Find Find 2. Determine the domain of each function. Express the domain in interval notation g( x) =
2x
x+2
h( x) =
3. Match each function with its graph. Write the function name (letter) beside the small Roman numeral of graph. i ii f ( x) = x g( x) = x 2 h( x) = x 3 s( x) = x x −2 w( x) =
iii x iv v Math 095
Midterm Exam 1
Show all your work.
Name: ______________________
Circle your answers.
1. Given these two points:(0, −2); (6, −4)
a. Determine the slope of the line
b. Write an equation of the line in slope-intercept form
c. Graph the line
2. What is the slope of the line that passes through the pairs of
points. (Hint: graph the points.)
a. (−1, 2), (6, 2)
b. (3, 2); (3, −2)
3. Write an equation in slope-intercept form for a line that passes
3
through the point (6, 3) and has a slope of
2
4. Determine if these lines are parallel, perpendicular or have some
other relationship:
3x  2 y  12
2x  3y  9
Factor the following polynomials completely.
Check your factoring by F.O.I.L.
y 2  y  12
5.
8.
6.
7.
8x2  x  9
8x2  6 x  1
9.
x 4  16
10.
25 y  y 3
y 3  64
Solve the following equations using the zero product rule
Check your solutions in the original equations.
11.
( x  9)(2 x  4)  0
12.
14  y (9  y )
13.
x3  9 x  0
14. Determine if the ordered pair is a solution to the system:
 1,  1
5 x  7 y  12
y  2 x  3
15. Solve this system by graphing.
State solution as an ordered pair.
4 x  2 y  4
3x  y  2
Solve the following systems by any method you prefer.
State answer as an ordered pair.
16.
8 y  4 x  16
9 y  3x  18
17.
1
1
13
x y
3
6
6
1
( x  4)  y  5
3
18. Find the function value for f (4) given f ( x)  6 x 2  4
19.
State the domain of these functions properly.
x  10
g ( x)  x  8
a.
b.
x  11
20. For questions A through E, refer to the graph below.
Use nearest whole value if it appears to be close to a grid line.
y  f (x)
y
x
A. Find f (1)
B. Find f (4)
C. Write the domain of f
D. Write the range of f
E. Find the X-intercept of the function
4
6
4
Math 095 Final Exam Winter 2009 Name: _________________________________ Show all work for full credit. Circle your answers. 1.
Write this equation in slope‐intercept form: 4 x − 3 y = 9 Identify the slope: y‐intercept: Graph the line. 2.
Use the point‐slope formula to write an equation of the line given the following information. The slope is 3, and the line passes through the point (–2, –5). Write the final answer in slope‐
intercept form. Graph the line. 3.
Solve this system of equations by graphing: 4 x − 2 y = −4
3x + y = 7
4.
To attend a state fair, the cost is $10 per person admission. There is an additional cost of $1.50 per ride. Write an equation that gives the total cost, y, of visiting the state fair and going on x rides. Use the equation to determine the cost of going to the state fair and going on 10 rides. Write the answers to these systems as ordered pairs. Circle your answers. 5.
7.
Solve this system of equations by 3 x + 5 y = 13
substitution: y = x+9
6x + 8 y = 5
3x − 2 y = 1
f ( x) =
b.
g( x) =
x −5
x+7
x +2 8.
h( x) = −3 x − 1 a. Find h(0) For the function: Solve this system of equations:
a.
6.
Write the domain of these functions in interval notation: b. Find h(−2) c. Graph the function Circle your answers 9.
Factor this polynomial:
9 y2 + 6 y + 1 10.
11.
12.
Factor this polynomial:
w2 + 12w + 35 Factor this polynomial: 18 x2 + 39 x − 15 Solve this equation for y:
7 y 2 − 9 y − 10 = 0 13.
Solve this equation for w:
3 w2 + 4 = 20w (
)
14.
Reduce to lowest terms:
x2 − 2 x − 3
x2 − 9
15.
Divide as indicated. Simplify to lowest terms
y2 + 8 y + 7 y + 7
÷
y2 − 2 y − 3 3 − y
Be sure to circle your answers 16.
20.
Simplify this radical: 4 32 x 6 21.
Add and subtract as indicated:
Solve this equation for w:
w w+3
3
−
=− 5
w
w
17.
x ⋅ 3 16 x 2 − 4 ⋅ 3 2 x 5 + 5 x ⋅ 3 54 x 2 Circle the statements that are true: h2 + k 2 = h + k a.
b.
h
m
=
n
( h) n
m
(h + k )2
c.
= h+ k 18.
Simplify this expression. Write with positive rational exponents only.
⎛ 1 ⎞
⎜⎜
⎟⎟
⎝ 16 ⎠
−3
4
⎛1⎞
− ⎜⎜ ⎟⎟
⎝8⎠
−2
3
19.
Simplify this radical: 108 22.
Multiply the radicals and simplify the answer: (2
)(
)
x −3 2 x +3 Be sure to check your possible solutions. Circle those that are true solutions. 23.
Solve the radical equation if possible:
26.
− 25 x−6 −5 = 0 24.
27.
Simplify the power of i: i101 28.
Multiply. Write the final answer in the form a + bi :
(4 + 3i )(2 − 4i ) Solve the radical equation if possible. Use the area to the right to check your possible solutions. See above. 8 y + 1 = − y − 13 25.
Solve the radical equation if possible:
w + 2 = 1 − 2w + 5 Rewrite the expression in terms of i: Be sure to circle your answers 29.
32.
30.
Solve this equation using the square root property:
x 2 = −81 f (x ) = −2(x − 5) − 5 2
Solve this equation using the square root property: 3( y − 4) = 15 2
31.
33.
Solve this equation using the quadratic formula: w2 − 4 w + 1 = 0 Graph this function: Solve this equation by any method:
3 x ( x − 3) = x − 8